Final answer:
The angle such that cos(theta) = √3/2 is 30 degrees, as this well-known trigonometric value corresponds to the cosine of a 30-60-90 triangle's 30-degree angle.
Step-by-step explanation:
To determine the angle such that cos(theta) = √3/2, we need to identify the angle within the unit circle where the cosine value corresponds to √3/2. Cosine is the ratio of the adjacent side to the hypotenuse in a right-angled triangle, and its value is positive in the first and fourth quadrants. The angles with a cosine of √3/2 are 30 degrees and 330 degrees (360 - 30), but since we are only provided choices within the range of 0 to 180 degrees, the correct answer is 30 degrees (option a).
Cosine values are well-known for certain reference angles, where the ratio of sides in special triangles, such as the 30-60-90 triangle, gives us these commonly recognized values. Since cos(30°) = √3/2, this is the correct angle choice from the given options.